Core 2 Abstract Theory Core: Multiscale models for mechano-chemical phenomena in liver cancer Provide an abstract/summary for the proposed Shared Resource Core, including which Research Projects will be supported by the Core. The three members of the theoretical physics core will support all three projects with theory and computation. Radhakrishnan uses computational chemistry to develop models at the molecular scale and then multiscale modeling algorithms to explore molecular effects at larger scales. Shenoy conducts discrete finite element calculations and coarse-grains to develop continuum models for the elastic and viscous response of the extracellular matrix (ECM) and the interaction between cells and the ECM. Liu uses analytical theory and computation to construct and study continuum models of active matter that apply at scales ranging from the cellular to the tissue level. Cells respond to mechanical stresses in their environment via a complex interplay between mechanics and biochemistry. Each of the three projects proposed for PSoC@Penn addresses this interplay. Project 1 addresses the effect of increased liver tissue stiffness on the malignant transformation of hepatocytes. Theoretical support for this project (Core-2/Aim-1) will focus on understanding the physical mechanisms underlying the causal relation between mechanical changes to the liver and the development of HCC. Project 2 advocates and tests a provocative hypothesis for mechano-transduction of the effect of the physical microenvironment in hepatocellular carcinoma (HCC) on the altered specificity of subcellular signals in hepatocytes and stromal cells, and its consequences for cell fate. Aim 2 of Core-2 interfaces directly with Project 2, which is model-driven with bidirectional coupling and iterative feedback between theory and experiment. Project 3 investigates the hypothesis that dysregulation of nuclear structure proteins contributes to disease. Core-2/Aim-3(a), which focuses on cell migration through pores and the extracellular matrix, is directly tied to Project-3/Aim-2. Core-2/Aim-3(b) focuses on DNA repair, also addressed experimentally in Project-3/Aim-2. The theory core will be held together via close collaboration among the theorists, and will be integrated into all three projects via collaboration with team members. The role of the core will not only be to provide theoretical support in analyzing and interpreting experimental data, but also to develop ideas in tandem with other members of PSoC@Penn to shape directions of inquiry as the project progresses. 22